Speeds of a boat along the current and against the current are 10 km/hr and 8 km/hr respectively. What is the speed (in km/hr) of the current?

Options

A. 1
B. 2
C. 3
D. 9

Answer

To solve the problem, we need to establish the relationship between the speed of the boat in still water, the speed of the current, and the speeds of the boat along and against the current.

1. **Define Variables**:
- Let the speed of the boat in still water be \( x \) km/hr.
- Let the speed of the current be \( y \) km/hr.

2. **Set Up Equations**:
- When the boat is moving along the current, its effective speed is the sum of the boat's speed in still water and the current's speed:
\[ x + y = 10 \quad \text{(1)} \]
- When the boat is moving against the current, its effective speed is the difference between the boat's speed in still water and the current's speed:
\[ x - y = 8 \quad \text{(2)} \]

3. **Solve the Equations**:
- We can solve these two equations simultaneously.
- First, we can add equations (1) and (2):
\[ (x + y) + (x - y) = 10 + 8 \]
This simplifies to:
\[ 2x = 18 \]
Thus, we find:
\[ x = 9 \quad \text{(speed of the boat in still water)} \]

- Now, we can substitute \( x \) back into equation (1) to find \( y \):
\[ 9 + y = 10 \]
Solving for \( y \):
\[ y = 10 - 9 = 1 \quad \text{(speed of the current)} \]

4. **Conclusion**:
- The speed of the current is \( 1 \) km/hr.

### Summary of Steps:
1. Define variables for the speed of the boat in still water and the speed of the current.
2. Set up equations based on the given speeds along and against the current.
3. Solve the equations simultaneously to find the speed of the boat in still water.
4. Substitute back to find the speed of the current.